Final answer:
To divide (n^2 + n - 3) by (n - 2), divide the first terms to find the quotient's first term, multiply the entire divisor by this term, subtract it from the original polynomial, and repeat until all terms are covered.
Step-by-step explanation:
To divide the polynomial (n^2 + n - 3) by (n - 2) using long division, you start by dividing the first term in the numerator by the first term in the divisor. In this case, you divide n^2 by n to get n.
After finding the first term of the quotient, you multiply the entire divisor by that term and subtract the result from the original polynomial. You bring down the next term, if any, and repeat the process until all terms are dealt with.
The result is a quotient polynomial and possibly a remainder. The key to mastering this process is understanding exponents and the basic rules of division. When dividing terms with the same base, you subtract the exponents.